Autoregressive fractionally integrated moving average (ARFIMA) is a type of mathematical model used to describe time-series data, like sales figures for a business, water levels in a river, or stock prices. It uses a combination of two types of data—autoregressive (AR) and fractionally integrated moving average (FIMA) data—to provide a better representation of the underlying pattern in the data. AR models look for patterns in the data over specific time intervals, while FIMA looks for patterns over different timescales. ARFIMA combines these two models to provide a more accurate representation of the overall pattern in the data.